Evaluate the integral using the given substitution.
-$$\int \frac { 8 s ^ { 3 } d s } { \sqrt { 3 - s ^ { 4 } } } , u = 3 - s ^ { 4 }$$
A) $- 4 \sqrt { 3 - s ^ { 4 } } + C$
B) $- 4 s ^ { 3 } \sqrt { 3 - s ^ { 4 } } + C$
C) $\frac { - 2 } { 2 \sqrt { 3 - s ^ { 4 } } } + C$
D) $\frac { 4 \mathrm {~s} ^ { 4 } } { \sqrt { 3 - \mathrm { s } ^ { 4 } } }$

Question

Quizplus · Accepted Answer

Given $u = 3 - s^4$, the derivative $du = -4s^3 ds$. The integral becomes $\int \frac{-du}{\sqrt{u}}$, which evaluates to $-2u^{1/2} + C = -2\sqrt{3 - s^4} + C$. Multiplying by 2 gives the correct answer.

Evaluate the Integral Using the Given Substitution ∫8s3ds3−s4,u=3−s4\int \frac { 8 s ^ { 3 } d s } { \sqrt { 3 - s ^ { 4 } } } , u = 3 - s ^ { 4 }∫3−s4​8s3ds​,u=3−s4

Evaluate the Integral Using the Given Substitution $\int \frac { 8 s ^ { 3 } d s } { \sqrt { 3 - s ^ { 4 } } } , u = 3 - s ^ { 4 }$